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Integration of Trigonometric Functions

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Question

Evaluate $\int \frac{sin (x + a) d x}{cos x}$

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Solution

$S i n (x + a) = S i n x . C o s a + C o s x . S i n a$

$\int \frac{S i n x . C o s a + C o s x . S i n a}{C o s x} d x = \int (T a n x . C o s a + S i n a) d x$

$= l n (S e c x + T a n x) . C o s a + S i n a . x + c$

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